A hybrid analytical model for the packing of frictional spheroidal particles

The packing of nonspherical particles remains a fundamental challenge in granular physics and powder technology because particle shape and interparticle friction jointly control packing density, porosity and microstructure. Existing excluded-volume models successfully describe many aspects of frictional particle packings but do not fully reproduce the characteristic densification peak observed for spheroids near unit aspect ratio. In this study, we develop a friction-dependent analytical model for the packing fraction of isotropically packed spheroidal particles by extending a literature based excluded-volume framework. The model combines an excluded-volume baseline with an additional shape-dependent rotational correction identified using symbolic regression, while a friction-dependent master curve is used to interpolate continuously between random loose and random close packing limits. The resulting formulation spans aspect ratios from highly oblate to highly prolate spheroids and reproduces the characteristic non-monotonic variation of packing fraction with particle shape, including near-sphere densification, the decline in packing efficiency at extreme aspect ratios, and the observed asymmetry between oblate and prolate packings. Model predictions show good agreement with published experimental and simulation datasets across a wide range of aspect ratios and friction states. The proposed framework provides a compact and physically interpretable alternative to computationally intensive simulations for practical application and testing.